A Chvátal-Erdős condition for (1,1)-factors in digraphs (Q1071779)

The authors prove: ''Let D be a k-connected digraph on at least two vertices such that \(k\geq \alpha (D)+p\). Then any set of vertex disjoint paths of D of total length at most p are contained in a (1,1)-factor of D.'' They conjecture: ''If D is a k-connected oriented graph on n vertices, with more than \((n(n-1)-k(k+1))/2\) arcs, then D is hamiltonian.''